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In this study we examine the tonal organization of a series of recordings of liturgical chants, sung in 1966 by the Georgian master singer Artem Erkomaishvili. This dataset is the oldest corpus of Georgian chants from which the time synchronous F0-trajectories for all three voices have been reliably determined (Müller et al. 2017). It is therefore of outstanding importance for the understanding of the tuning principles of traditional Georgian vocal music.
The aim of the present study is to use various computational methods to analyze what these recordings can contribute to the ongoing scientific dispute about traditional Georgian tuning systems. Starting point for the present analysis is the re-release of the original audio data together with estimated fundamental frequency (F0) trajectories for each of the three voices, beat annotations, and digital scores (Rosenzweig et al. 2020). We present synoptic models for the pitch and the harmonic interval distributions, which are the first of such models for which the complete Erkomaishvili dataset was used. We show that these distributions can be very compactly be expressed as Gaussian mixture models, anchored on discrete sets of pitch or interval values for the pitch and interval distributions, respectively. As part of our study we demonstrate that these pitch values, which we refer to as scale pitches, and which are determined as the mean values of the Gaussian mixture elements, define the scale degrees of the melodic sound scales which build the skeleton of Artem Erkomaishvili’s intonation. The observation of consistent pitch bending of notes in melodic phrases, which appear in identical form in a group of chants, as well as the observation of harmonically driven intonation adjustments, which are clearly documented for all pure harmonic intervals, demonstrate that Artem Erkomaishvili intentionally deviates from the scale pitch skeleton quite freely. As a central result of our study, we proof that this melodic freedom is always constrained by the attracting influence of the scale pitches. Deviations of the F0-values of individual note events from the scale pitches at one instance of time are compensated for in the subsequent melodic steps. This suggests a deviation-compensation mechanism at the core of Artem Erkomaishvili’s melody generation, which clearly honors the scales but still allows for a large degree of melodic flexibility. This model, which summarizes all partial aspects of our analysis, is consistent with the melodic scale models derived from the observed pitch distributions, as well as with the melodic and harmonic interval distributions. In addition to the tangible results of our work, we believe that our work has general implications for the determination of tuning models from audio data, in particular for non-tempered music.
Modern natural hazards research requires dealing with several uncertainties that arise from limited process knowledge, measurement errors, censored and incomplete observations, and the intrinsic randomness of the governing processes. Nevertheless, deterministic analyses are still widely used in quantitative hazard assessments despite the pitfall of misestimating the hazard and any ensuing risks.
In this paper we show that Bayesian networks offer a flexible framework for capturing and expressing a broad range of uncertainties encountered in natural hazard assessments. Although Bayesian networks are well studied in theory, their application to real-world data is far from straightforward, and requires specific tailoring and adaptation of existing algorithms. We offer suggestions as how to tackle frequently arising problems in this context and mainly concentrate on the handling of continuous variables, incomplete data sets, and the interaction of both. By way of three case studies from earthquake, flood, and landslide research, we demonstrate the method of data-driven Bayesian network learning, and showcase the flexibility, applicability, and benefits of this approach.
Our results offer fresh and partly counterintuitive insights into well-studied multivariate problems of earthquake-induced ground motion prediction, accurate flood damage quantification, and spatially explicit landslide prediction at the regional scale. In particular, we highlight how Bayesian networks help to express information flow and independence assumptions between candidate predictors. Such knowledge is pivotal in providing scientists and decision makers with well-informed strategies for selecting adequate predictor variables for quantitative natural hazard assessments.
This study presents an unsupervised feature selection and learning approach for the discovery and intuitive imaging of significant temporal patterns in seismic single-station or network recordings. For this purpose, the data are parametrized by real-valued feature vectors for short time windows using standard analysis tools for seismic data, such as frequency-wavenumber, polarization, and spectral analysis. We use Self-Organizing Maps (SOMs) for a data-driven feature selection, visualization and clustering procedure, which is in particular suitable for high-dimensional data sets. Our feature selection method is based on significance testing using the Wald-Wolfowitz runs test for-individual features and on correlation hunting with SOMs in feature subsets. Using synthetics composed of Rayleigh and Love waves and real-world data, we show the robustness and the improved discriminative power of that approach compared to feature subsets manually selected from individual wavefield parametrization methods. Furthermore, the capability of the clustering and visualization techniques to investigate the discrimination of wave phases is shown by means of synthetic waveforms and regional earthquake recordings.